# Thread: Could an Earthlike planet reasonably have two Luna-sized Moons?

1. ## Could an Earthlike planet reasonably have two Luna-sized Moons?

Assuming the planet is human-habitable and of similar size and gravity as Earth.

If so, what would be the effect on tides?

2. Possibly, but from what I've been told, such worlds would be exceedingly rare.

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As for the reasonableness of it, I have certainly entertained far less likely scenarios.

The tides would depend on how the orbits were arranged. In the very unlikely scenario where I the two moons were at mutual Lagrange points (it might be more likely that they are close enough to orbit each other) they would have the same orbital period, and the earth would have a monthly pattern of daily tides similar to what we have now.

It is far more likely that the moons would be at different radii, giving two monthly period. Since the objects are similarly sized, the closer object would dominate the tides.

If one object is twice as large as the other, and at a radius of 1.7 times the radius of the smaller inner moon (with a period of 2.22 times the inner moon) the tidal effects of the two would be comparable. The tides would add when the moons aligned (once every 1.82 months, by the inner moons , much like how the tides from the Sun and Moon add now during a full and new moon.

On our fictitious planet, a particularly high tide would occur when the moons aligned near a full or new stage in their orbits. This would not produce high enough tides compared to normal lunar alignments to threaten a civilization (storm surges cause a much greater change in water level). Since each alignment recedes by roughly 65 degrees each alignment, this would happen roughly once a year.

Thus would be the tides on a planet with a Lunar sized object at 1.7 times the distance to the Moon, with an additional object half as massive at the Lunar distance.

4. I don't think that a pair of moons could orbit each other. If they are both the same distance from the planet they will probabaly collide in the long run, or have a complicated relationship like Saturn's moons Janus and Epimetheus
http://en.wikipedia.org/wiki/Epimeth...heus_and_Janus
where the two moons have slightly different orbits, and swap orbits with each other at regular intervals, by trading momentum.

5. It's not easy to determine the long-term stability of a system comprising an Earth-sized planet with two Moon-sized satellites; I suspect that most such systems won't be stable. For a system to have reasonably long-term stability (say a billion years), the two satellites would almost certainly have to be in resonance with each other. I don't think a configuration where the moons are in each others Langrange points would be stable due to solar influence.

So, the orbital mechanics don't preclude the system you propose, but they make it quite unlikely.

The second problem is related to the system's formation. Current thought is that the Moon formed from debris left behind after Earth was struck by a very large (possibly Mars-sized) object. The accretion of two moons from the resulting debris field is, I guess, possible, but improbable.

To a first approximation, the tides from the two moons can be superimposed, like the lunar and solar tides are on Earth. There are a lot of papers (many even useful) on arXiv.org (it's not refereed.....), such as http://arxiv.org/abs/1205.3536 , which model body-tide interactions.

If you're doing this for a story, I'd not worry about the formation -- that can always be hand-waved away by having a couple of people ooh and aah about how improbable it is -- but I would worry about the orbital mechanics. Keep them out of each other's Hill sphere relative to the planet, keep them both within the planet's Hill sphere relative to its primary, and have them both orbiting so that the period of the closer one is longer than the planetary day (I've read that this results in a transfer of angular momentum from the satellite to the primary, which means that the satellite's orbit is getting increasingly close to the primary's surface. This could be bad....), and have them in a fairly simple resonance, like 2:1 or 3:2, and it's likely to be plausible enough so nobody is jarred. Oh, and no retrograde orbits. They may be stable, but you'll have the joy of exploring that particular configuration space .

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The smaller worlds Mars and Pluto have more than one moon. Why would it be rare for two luna sized satellites to orbit other earths?

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Originally Posted by Cosmologist
The smaller worlds Mars and Pluto have more than one moon. Why would it be rare for two luna sized satellites to orbit other earths?
Mars' moons are much smaller than Luna. Larger moons (relative to the mass of the planet) make the orbits less stable.

Considering the case of two self gravitating moons:

This would require the moons to be within their Hill sphere. For two Luna sized objects orbiting an Earth sized planet the combined Hill sphere of the moons would be 73.3 KM, with a radius for each moon of 1.7 KM. The moons would have to be a handful of radii away from each other, suggesting they should have collided a long time ago.

The tides caused by moons in horseshoe orbits would be interesting. The tides would be maximum when they are opposed, and the moons would never be in conjunction.

8. Jupiter and the Galileans are stable. Suppose a system where that setup is simply scaled down by a factor of ten, diameters and orbits, is that plausible or stable?

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Originally Posted by agingjb
Jupiter and the Galileans are stable. Suppose a system where that setup is simply scaled down by a factor of ten, diameters and orbits, is that plausible or stable?
The largest of the Galilean moons are about twice the size of Luna.
Scale it down ten times and those moons would be significantly smaller than Luna; probably stable, but not Lunar-sized.

10. One thing that has me curious, is the tidal acceleration causing increasing lunar distances. If both moons were equal sized, would they recede at the same rate? Would there be a point where they have receded enough for their own gravity to cause orbital stability problems?

11. Originally Posted by swampyankee
The second problem is related to the system's formation. Current thought is that the Moon formed from debris left behind after Earth was struck by a very large (possibly Mars-sized) object. The accretion of two moons from the resulting debris field is, I guess, possible, but improbable.
Perhaps a Not Quite As Giant Impact carved out the second moon later. Or maybe it carved out a moon from the original moon. I wonder if a Giant Impact could create two moons at one time, if two globs could have held together to coalesce in different orbits.

That makes me wonder. What if Earth already had a moon from a big impact or co-accretion when it was smacked by Theia... or if Theia smacked that moon first?

12. I remember an Asimov piece where he discussed the relative sizes of the earth and it's moon. IIRC he came to the conclusion that for such a big moon to form where it is, gravitationally speaking relative to the earth and the sun, couldn't be explanable by any captured debris. He suggested that perhaps the earth had a twin or similar sized neighbour, around a barycentric orbit which collapsed resulting in one large dense planet with a smaller less dense moon. In such a situation, I don't think there could be a 3rd place position after the impact.

ETA. I went to look at wiki for some barycentre information and the last animation here shows quite a large potential for catastrophy
Last edited by headrush; 2012-Jul-27 at 04:31 PM. Reason: ETA

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If it was for a story...
I would ask what is it you need out of the story that requires 2 moons "of the same size"? If the need to be the same mass because of... people settling on them similarly or whatnot, they do not need to be in the same orbital distance... one could be farther away than the other.

If dramatically you wanted someone to look up in the sky at 2 equally large moons, well, perspectivewise the moons could be at 2 different orbits and be 2 different sizes, just the smaller moon is closer and so appears the same size as the other.

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A web comic I follow is the fantasy Tales of the Questor, set on an Earth-like planet with two large moons, the larger one farther out, with ten and thirty day periods.
The artist went through the trouble to run a simulation of this system for a long time, to check its stability (nice since he is a YEC and global warming denier).

15. Originally Posted by PlutonianEmpire
One thing that has me curious, is the tidal acceleration causing increasing lunar distances. If both moons were equal sized, would they recede at the same rate? Would there be a point where they have receded enough for their own gravity to cause orbital stability problems?
The Earth-Moon system is rotating about the common center of mass, and the Earth is also rotating about its center of mass. This combined system has a certain amount of angular momentum: that from the orbital motion of the Moon about the Earth-Moon center of mass (also called barycenter), and that from the Earth spinning around its axis. The Moon's tide induces a torque onto the Earth which tends to slow the Earth's rotation. This reduces the Earth's angular momentum, but that angular momentum has to go someplace, and the only place it can go is into increasing the amount of angular momentum tied up in the Moon's orbital motion. This requires the Moon to speed up, which means it's orbital radius has to increase.

16. Originally Posted by swampyankee
The Earth-Moon system is rotating about the common center of mass, and the Earth is also rotating about its center of mass. This combined system has a certain amount of angular momentum: that from the orbital motion of the Moon about the Earth-Moon center of mass (also called barycenter), and that from the Earth spinning around its axis. The Moon's tide induces a torque onto the Earth which tends to slow the Earth's rotation. This reduces the Earth's angular momentum, but that angular momentum has to go someplace, and the only place it can go is into increasing the amount of angular momentum tied up in the Moon's orbital motion. This requires the Moon to speed up, which means it's orbital radius has to increase.
Yep, I know that already, I was just wondering if two large moons might cause trouble to each other or the planet after their orbital radii got too large or if they got larger at the same rates?

17. Originally Posted by JCoyote
If it was for a story...
I would ask what is it you need out of the story that requires 2 moons "of the same size"? If the need to be the same mass because of... people settling on them similarly or whatnot, they do not need to be in the same orbital distance... one could be farther away than the other.

If dramatically you wanted someone to look up in the sky at 2 equally large moons, well, perspectivewise the moons could be at 2 different orbits and be 2 different sizes, just the smaller moon is closer and so appears the same size as the other.
It's just for my curiousity. And they don't have to be at the same orbital distance-- I never even considered that they could be until utesfan brought it up.

18. Originally Posted by PlutonianEmpire
Yep, I know that already, I was just wondering if two large moons might cause trouble to each other or the planet after their orbital radii got too large or if they got larger at the same rates?
Look at the Galilean moons. This tugging is why they have developed resonances. They are predicted to change and to have changed over geologic and astronomical time, but for life-scale time (100s of millions to a billion years), it might be stable-ish even if changing.

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